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Rutherford Constant

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The Rutherford constant is a mathematical constant that arises in plasma physics and is defined by

K_R=sqrt(2)int_(-1)^infty([R(x)]^2)/(S[x])dx
(1)
=0.8227...,
(2)

where

R(x)=1/(2pi)int_(u^_)^(2pi-u^_)(cosudu)/(sqrt(x-cosu))
(3)
S(x)=1/(2pi)int_(u^_)^(2pi-u^_)(du)/(sqrt(x-cosu))
(4)

and

u^_={0 for x>1; cos^(-1)x for -1<x<1
(5)

(Samain 1984).

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References

Samain, A. "Diamagnetic Destabilization of Magnetic Islands In The Non-Linear Regime." Plasma Phys. Controlled Fusion 26, 731-747, 1984.

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Rutherford Constant

Cite this as:

Weisstein, Eric W. "Rutherford Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RutherfordConstant.html

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